Index
# Change directory
import os
os.chdir("../../../..")
# Import libraries
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import altair as alt
import random
import statsmodels.api as sm
from skfda.representation.grid import FDataGrid
from skfda.preprocessing.dim_reduction.projection import FPCA
from skfda.exploratory.visualization import FPCAPlot
from sklearn.preprocessing import OneHotEncoder
import skfda
from skfda.ml.regression import LinearRegression
from skfda.representation.basis import FDataBasis, FourierBasis
from skfda.exploratory.depth import IntegratedDepth, ModifiedBandDepth
from skfda.exploratory.visualization import Boxplot
# Import designed-functions
from helper_functions.window_extraction import Merge_data, process_sensor_data, align_to_zero, balance_index
from helper_functions.time_series_visualization import plot_all_time_series, plot_all_time_series_and_mean_fpca, plot_all_time_series_in_group
from helper_functions.functionalPCA import fpca_two_inputs, first_component_extraction, bootstrap, create_pc_scores_plots, visualize_regression
from helper_functions.functional_regression import Function_regression, coefficent_visualization
/var/folders/vh/dw36swbx2939r11_2dkm6r4m0000gn/T/ipykernel_67452/1250556825.py:9: DeprecationWarning: The module "projection" is deprecated. Please use "dim_reduction" from skfda.preprocessing.dim_reduction.projection import FPCA
The path of the files can be change based on where the data is stored.
# Import datasets
sensorA_System1 = pd.read_csv("RawData/System1_SensorA.csv")
sensorA_System2 = pd.read_csv("RawData/System2_SensorA.csv")
sensorB_System1 = pd.read_csv("RawData/System1_SensorB.csv")
sensorB_System2 = pd.read_csv("RawData/System2_SensorB.csv")
sensorA_System1_missing = pd.read_csv("RawData/SensorA_System1_missing values.csv")
sensorA_System2_missing = pd.read_csv("RawData/SensorA_System2_missing values.csv")
keyByTestID = pd.read_csv("RawData/Key by TestID.csv", parse_dates=['DateTime'])
# Transpose dataset to make columns as timestamps and rows as tests
# Sensor A
A1_transposed = sensorA_System1.T.reset_index()
A1_transposed.columns = A1_transposed.iloc[0]
A1_transposed.rename(columns={A1_transposed.columns[0]: 'TestID'}, inplace=True)
A1_transposed = A1_transposed.drop(0)
A1_transposed['TestID'] = A1_transposed['TestID'].astype(int)
A2_transposed = sensorA_System2.T.reset_index()
A2_transposed.columns = A2_transposed.iloc[0]
A2_transposed.rename(columns={A2_transposed.columns[0]: 'TestID'}, inplace=True)
A2_transposed = A2_transposed.drop(0)
A2_transposed['TestID'] = A2_transposed['TestID'].astype(int)
A1_missing_transposed = sensorA_System1_missing.T.reset_index()
A1_missing_transposed.columns = A1_missing_transposed.iloc[0]
A1_missing_transposed.rename(columns={A1_missing_transposed.columns[0]: 'TestID'}, inplace=True)
A1_missing_transposed = A1_missing_transposed.drop(0)
A1_missing_transposed['TestID'] = A1_missing_transposed['TestID'].astype(int)
A2_missing_transposed = sensorA_System2_missing.T.reset_index()
A2_missing_transposed.columns = A2_missing_transposed.iloc[0]
A2_missing_transposed.rename(columns={A2_missing_transposed.columns[0]: 'TestID'}, inplace=True)
A2_missing_transposed = A2_missing_transposed.drop(0)
A2_missing_transposed['TestID'] = A2_missing_transposed['TestID'].astype(int)
# Sensor B
B1_transposed = sensorB_System1.T.reset_index()
B1_transposed.columns = B1_transposed.iloc[0]
B1_transposed.rename(columns={B1_transposed.columns[0]: 'TestID'}, inplace=True)
B1_transposed = B1_transposed.drop(0)
B1_transposed['TestID'] = B1_transposed['TestID'].astype(int)
B2_transposed = sensorB_System2.T.reset_index()
B2_transposed.columns = B2_transposed.iloc[0]
B2_transposed.rename(columns={B2_transposed.columns[0]: 'TestID'}, inplace=True)
B2_transposed = B2_transposed.drop(0)
B2_transposed['TestID'] = B2_transposed['TestID'].astype(int)
# Complete A1 and A2 with the missing values
A1_transposed_mid = A1_transposed[~A1_transposed.TestID.isin(A1_missing_transposed.TestID)]
A1_transposed = pd.concat([A1_transposed_mid, A1_missing_transposed], axis=0)
A2_transposed_mid = A2_transposed[~A2_transposed.TestID.isin(A2_missing_transposed.TestID)]
A2_transposed = pd.concat([A2_transposed_mid, A2_missing_transposed], axis=0)
# Relabeling System Values
keyByTestID["System"] = keyByTestID["System"].replace({"System 2A":"System 2","System 2B":"System 2"})
# Create new column to fill fluid temperature NA's
# Note: Fluid temperature: If specified, take as the temperature of the sample fluid. The rest of the system temperature can be taken as ambient temperature.
keyByTestID['Fluid_Temperature_Filled'] = keyByTestID['Fluid Temperature'].combine_first(keyByTestID['AmbientTemperature'])
# Binning
# Categorize 'FluidType' into Blood and Aqueous
keyByTestID['FluidTypeBin'] = np.where(keyByTestID['FluidType'].str.startswith('Eurotrol'), 'Aqueous', 'Blood')
# Categorize 'AgeOfCardInDaysAtTimeOfTest' into bins
keyByTestID["CardAgeBin"] = pd.cut(keyByTestID["AgeOfCardInDaysAtTimeOfTest"], bins=[0, 9, 28, 56, 84, 112, 140, 168, 196, 224, 252],
labels=['[0-9]', '(9-28]', '(28-56]', '(56-84]', '(84-112]', '(112-140]', '(140-168]', '(168-196]', '(196-224]', '(224-252]'])
# Categorize 'Fluid_Temperature_Filled' into bins
keyByTestID["FluidTempBin"] = pd.cut(keyByTestID["Fluid_Temperature_Filled"], bins=[-1, 20, 25, 100], labels=['Below 20', '20-25', 'Above 25'])
# Filtering successful tests
keyByTestID = keyByTestID[keyByTestID['ReturnCode'].isin(['Success','UnderReportableRange'])]
# Merge dataset with keyByTestID and delete unmatched tests
keyByTestID['TestID'] = keyByTestID['TestID'].astype(int)
keyByTestID['System'] = keyByTestID['System'].astype(str)
A1_keyByTestID = keyByTestID[(keyByTestID['Sensor'] == 'Sensor A') & (keyByTestID['System'] == 'System 1')]
A1_Merged = pd.merge(A1_keyByTestID,A1_transposed,how='inner', on=['TestID'])
A1_transposed = A1_transposed[A1_transposed['TestID'].isin(A1_Merged['TestID'])]
A2_keyByTestID = keyByTestID.loc[(keyByTestID['Sensor'] == 'Sensor A') & (keyByTestID['System'] != 'System 1')]
A2_Merged = pd.merge(A2_keyByTestID,A2_transposed,how='inner', on=['TestID'])
A2_transposed = A2_transposed[A2_transposed['TestID'].isin(A2_Merged['TestID'])]
sensorA_System1 = sensorA_System1.loc[:, sensorA_System1.columns.isin(A1_Merged['TestID'].astype(str))]
sensorA_System2 = sensorA_System2.loc[:, sensorA_System2.columns.isin(A2_Merged['TestID'].astype(str))]
B1_keyByTestID = keyByTestID[(keyByTestID['Sensor'] == 'Sensor B') & (keyByTestID['System'] == 'System 1')]
B1_Merged = pd.merge(B1_keyByTestID,B1_transposed,how='inner', on=['TestID'])
B1_transposed = B1_transposed[B1_transposed['TestID'].isin(B1_Merged['TestID'])]
B2_keyByTestID = keyByTestID.loc[(keyByTestID['Sensor'] == 'Sensor B') & (keyByTestID['System'] != 'System 1')]
B2_Merged = pd.merge(B2_keyByTestID,B2_transposed,how='inner', on=['TestID'])
B1_transposed = B2_transposed[B2_transposed['TestID'].isin(A2_Merged['TestID'])]
sensorB_System1 = sensorB_System1.loc[:, sensorB_System1.columns.isin(B1_Merged['TestID'].astype(str))]
sensorB_System2 = sensorB_System2.loc[:, sensorB_System2.columns.isin(B2_Merged['TestID'].astype(str))]
print('A1: ', A1_Merged.shape)
print('A2: ', A2_Merged.shape)
print('B1: ', B1_Merged.shape)
print('B2: ', B2_Merged.shape)
A1: (3382, 3380) A2: (7743, 3371) B1: (3375, 3380) B2: (7745, 3371)
# Note: Only run once. If not, restart the kernel and run from the beggining again.
A1_Merged = A1_Merged[A1_Merged["TestID"].isin(B1_Merged["TestID"])]
B1_Merged = B1_Merged[B1_Merged["TestID"].isin(A1_Merged["TestID"])]
A2_Merged = A2_Merged[A2_Merged["TestID"].isin(B2_Merged["TestID"])]
B2_Merged = B2_Merged[B2_Merged["TestID"].isin(A2_Merged["TestID"])]
print('A1: ', A1_Merged.shape)
print('A2: ', A2_Merged.shape)
print('B1: ', B1_Merged.shape)
print('B2: ', B2_Merged.shape)
A1: (3374, 3380) A2: (7743, 3371) B1: (3374, 3380) B2: (7743, 3371)
# Match window values of Sensor A and B for each test
# Sensor A
calDelimit = 11
cal_window_size = 8
sampleDelimit = 15
sample_window_size = 5
A1_cal_window, A1_sample_window = process_sensor_data(A1_Merged, calDelimit, cal_window_size, sampleDelimit, sample_window_size)
A2_cal_window, A2_sample_window = process_sensor_data(A2_Merged, calDelimit, cal_window_size, sampleDelimit, sample_window_size)
# sensor B
calDelimit = 20
cal_window_size = 18
sampleDelimit_blood = 24
sampleDelimit_aqueous = 30
sample_window_size = 4
B1_cal_window, B1_sample_window = process_sensor_data(B1_Merged, calDelimit, cal_window_size, sampleDelimit_blood, sample_window_size, sampleDelimit_aqueous)
B2_cal_window, B2_sample_window = process_sensor_data(B2_Merged, calDelimit, cal_window_size, sampleDelimit_blood, sample_window_size, sampleDelimit_aqueous)
A1_cal_window_drop_index = A1_cal_window.loc[A1_cal_window.isna().sum(axis=1)!=0].index
A2_cal_window_drop_index = A2_cal_window.loc[A2_cal_window.isna().sum(axis=1)!=0].index
A1_sample_window_drop_index = A1_sample_window.loc[A1_sample_window.isna().sum(axis=1)!=0].index
A2_sample_window_drop_index = A2_sample_window.loc[A2_sample_window.isna().sum(axis=1)!=0].index
B1_cal_window_drop_index = B1_cal_window.loc[B1_cal_window.isna().sum(axis=1)!=0].index
B2_cal_window_drop_index = B2_cal_window.loc[B2_cal_window.isna().sum(axis=1)!=0].index
B1_sample_window_drop_index = B1_sample_window.loc[B1_sample_window.isna().sum(axis=1)!=0].index
B2_sample_window_drop_index = B2_sample_window.loc[B2_sample_window.isna().sum(axis=1)!=0].index
# Check if missing values in different windows is different
print("The missing value in calibration window:",A1_cal_window_drop_index)
print("The missing value in sample window:",A1_sample_window_drop_index)
print("The missing value in calibration window:",A2_cal_window_drop_index)
print("The missing value in sample window:",A2_sample_window_drop_index)
print("The missing value in calibration window:",B1_cal_window_drop_index)
print("The missing value in sample window:",B1_sample_window_drop_index)
print("The missing value in calibration window:",B2_cal_window_drop_index)
print("The missing value in sample window:",B2_sample_window_drop_index)
The missing value in calibration window: Float64Index([], dtype='float64', name='TestID') The missing value in sample window: Float64Index([], dtype='float64', name='TestID') The missing value in calibration window: Int64Index([], dtype='int64', name='TestID') The missing value in sample window: Int64Index([], dtype='int64', name='TestID') The missing value in calibration window: Float64Index([], dtype='float64', name='TestID') The missing value in sample window: Float64Index([], dtype='float64', name='TestID') The missing value in calibration window: Float64Index([], dtype='float64', name='TestID') The missing value in sample window: Float64Index([], dtype='float64', name='TestID')
# Set index for Merge datasets
A1_Merged.set_index("TestID", inplace=True)
A2_Merged.set_index("TestID", inplace=True)
B1_Merged.set_index("TestID", inplace=True)
B2_Merged.set_index("TestID", inplace=True)
# Find missing value
print("The problem indexes after extract the window are:",A1_Merged.index.difference(A1_cal_window.index))
print("The problem indexes after extract the window are:",A1_Merged.index.difference(A1_sample_window.index))
print("The problem indexes after extract the window are:",A2_Merged.index.difference(A2_cal_window.index))
print("The problem indexes after extract the window are:",A2_Merged.index.difference(A2_sample_window.index))
print("The problem indexes after extract the window are:",B1_Merged.index.difference(B1_cal_window.index))
print("The problem indexes after extract the window are:",B1_Merged.index.difference(B1_sample_window.index))
print("The problem indexes after extract the window are:",B2_Merged.index.difference(B2_cal_window.index))
print("The problem indexes after extract the window are:",B2_Merged.index.difference(B2_sample_window.index))
A1_Merged = A1_Merged.drop(A1_Merged.index.difference(A1_cal_window.index))
A1_Merged = A1_Merged.drop(A1_Merged.index.difference(A1_sample_window.index))
A2_Merged = A2_Merged.drop(A2_Merged.index.difference(A2_cal_window.index))
A2_Merged = A2_Merged.drop(A2_Merged.index.difference(A2_sample_window.index))
B1_Merged = B1_Merged.drop(B1_Merged.index.difference(B1_cal_window.index))
B1_Merged = B1_Merged.drop(B1_Merged.index.difference(B1_sample_window.index))
B2_Merged = B2_Merged.drop(B2_Merged.index.difference(B2_cal_window.index))
B2_Merged = B2_Merged.drop(B2_Merged.index.difference(B2_sample_window.index))
# Clear the Nan in index of sensor A
A1_cal_window = A1_cal_window[~A1_cal_window.index.isna()]
A1_sample_window = A1_sample_window[~A1_sample_window.index.isna()]
A2_cal_window = A2_cal_window[~A2_cal_window.index.isna()]
A2_sample_window = A2_sample_window[~A2_sample_window.index.isna()]
# Clear the Nan in index of sensor B
B1_cal_window = B1_cal_window[~B1_cal_window.index.isna()]
B1_sample_window = B1_sample_window[~B1_sample_window.index.isna()]
B2_cal_window = B2_cal_window[~B2_cal_window.index.isna()]
B2_sample_window = B2_sample_window[~B2_sample_window.index.isna()]
The problem indexes after extract the window are: Int64Index([12470355, 12470361, 12470365, 12537663, 12539049, 12622570], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([12470355, 12470361, 12470365, 12537663, 12539049, 12622570], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([12622570], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([12622570], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([3518677, 3518678], dtype='int64', name='TestID') The problem indexes after extract the window are: Int64Index([3518677, 3518678], dtype='int64', name='TestID')
# Shape of the subsets of time series after the extraction from the windows
# Cal Window
print('Shape of the time series after extraction')
print('A1_cal_window: ', A1_cal_window.shape)
print('A2_cal_window: ', A2_cal_window.shape)
print('B1_cal_window: ', B1_cal_window.shape)
print('B2_cal_window: ', B2_cal_window.shape)
# Sample Window
print('A1_sample_window: ', A1_sample_window.shape)
print('A2_sample_window: ', A2_sample_window.shape)
print('B1_sample_window: ', B1_sample_window.shape)
print('B2_sample_window: ', B2_sample_window.shape)
# We can delete the unmatch index but it is not necessary
Shape of the time series after extraction A1_cal_window: (3368, 41) A2_cal_window: (7743, 41) B1_cal_window: (3373, 91) B2_cal_window: (7741, 91) A1_sample_window: (3368, 26) A2_sample_window: (7743, 26) B1_sample_window: (3373, 21) B2_sample_window: (7741, 21)
# Cal Window
A1_cal_window_zero = align_to_zero(A1_cal_window)
A2_cal_window_zero = align_to_zero(A2_cal_window)
B1_cal_window_zero = align_to_zero(B1_cal_window)
B2_cal_window_zero = align_to_zero(B2_cal_window)
# Sample Window
A1_sample_window_zero = align_to_zero(A1_sample_window)
A2_sample_window_zero = align_to_zero(A2_sample_window)
B1_sample_window_zero = align_to_zero(B1_sample_window)
B2_sample_window_zero = align_to_zero(B2_sample_window)
# Combine data: Merge the zero-aligned time series with "FluidType", "AgeOfCardInDaysAtTimeOfTest", "Fluid_Temperature_Filled", "FluidTypeBin", "CardAgeBin", "FluidTempBin"
A1_cal_window_combine = Merge_data(A1_cal_window_zero,A1_Merged)
A2_cal_window_combine = Merge_data(A2_cal_window_zero,A2_Merged)
B1_cal_window_combine = Merge_data(B1_cal_window_zero,B1_Merged)
B2_cal_window_combine = Merge_data(B2_cal_window_zero,B2_Merged)
## Sample window
A1_sample_window_combine = Merge_data(A1_sample_window_zero,A1_Merged)
A2_sample_window_combine = Merge_data(A2_sample_window_zero,A2_Merged)
B1_sample_window_combine = Merge_data(B1_sample_window_zero,B1_Merged)
B2_sample_window_combine = Merge_data(B2_sample_window_zero,B2_Merged)
System1_Index, System2_Index = balance_index(A1_cal_window_combine,A2_cal_window_combine,"CardAgeBin")
System1 Sensor A & B distribution: [0-9] 142 (9-28] 142 (28-56] 142 (56-84] 142 (84-112] 142 (112-140] 142 (140-168] 142 (168-196] 142 (196-224] 142 (224-252] 142 Name: CardAgeBin, dtype: int64 System2 Sensor A & B distribution: [0-9] 142 (9-28] 142 (28-56] 142 (56-84] 142 (84-112] 142 (112-140] 142 (140-168] 142 (168-196] 142 (196-224] 142 (224-252] 142 Name: CardAgeBin, dtype: int64
# Balanced data
A1_cal_window_combine_balanced = A1_cal_window_combine.loc[System1_Index]
A1_sample_window_combine_balanced = A1_sample_window_combine.loc[System1_Index]
A2_cal_window_combine_balanced = A2_cal_window_combine.loc[System2_Index]
A2_sample_window_combine_balanced = A2_sample_window_combine.loc[System2_Index]
B1_cal_window_combine_balanced = B1_cal_window_combine.loc[System1_Index]
B1_sample_window_combine_balanced = B1_sample_window_combine.loc[System1_Index]
B2_cal_window_combine_balanced = B2_cal_window_combine.loc[System2_Index]
B2_sample_window_combine_balanced = B2_sample_window_combine.loc[System2_Index]
# Plot all the balanced time series from the window extraction
plot_all_time_series_in_group(A1_cal_window_combine_balanced, A1_sample_window_combine_balanced, A2_cal_window_combine_balanced, A2_sample_window_combine_balanced, "CardAgeBin", "System 1A - CalWindow", "System 1A - SampleWindow","System 2A - CalWindow", "System 2A - SampleWindow")
# Plot all the balanced time series from the window extraction
plot_all_time_series_in_group(B1_cal_window_combine_balanced, B1_sample_window_combine_balanced, B2_cal_window_combine_balanced, B2_sample_window_combine_balanced, "CardAgeBin", "System 1B - CalWindow", "System 1B - SampleWindow","System 2B - CalWindow", "System 2B - SampleWindow")
The following seccion will introduce
pc_scores_s1_A_cal_window, pc_scores_s2_A_cal_window,fpca_s1_A_cal_window,fpca_s2_A_cal_window = fpca_two_inputs(A1_cal_window_combine_balanced.iloc[:,:-6], A2_cal_window_combine_balanced.iloc[:,:-6], color_fpc1_s1='tab:blue', color_fpc2_s1='tab:cyan', color_fpc1_s2='tab:orange', color_fpc2_s2='gold')
print("--------------------------------------------------- Bootstrap -------------------------------------------------------------------------------------------")
ac1, ac2 = bootstrap(A1_cal_window_combine_balanced, A2_cal_window_combine_balanced,"A","cal_window",features="CardAgeBin")
print("--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------")
create_pc_scores_plots(pc_scores_s1_A_cal_window, pc_scores_s2_A_cal_window, A1_cal_window_combine_balanced, A2_cal_window_combine_balanced,features="CardAgeBin")
S1 Explain variance PC1 (%): 99.87217788257936 S1 Explain variance PC2 (%): 0.03137443830513182 S2 Explain variance PC1 (%): 99.93904177973562 S2 Explain variance PC2 (%): 0.022619270205938954 The time series contributing most to PC1 is at index 800 with TestID 12529762.0 The time series contributing most to PC2 is at index 82 with TestID 12615989.0 The time series contributing most to PC1 is at index 91 with TestID 3568638 The time series contributing most to PC2 is at index 19 with TestID 3559978
--------------------------------------------------- Bootstrap ------------------------------------------------------------------------------------------- Confidence Interval of 1st component The number of sampling is 142 The boxplot of 1st Component
--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------
pc_scores_s1_A_sample_window, pc_scores_s2_A_sample_window,fpca_s1_A_sample_window,fpca_s2_A_sample_window = fpca_two_inputs(A1_sample_window_combine_balanced.iloc[:,:-6], A2_sample_window_combine_balanced.iloc[:,:-6], color_fpc1_s1='tab:blue', color_fpc2_s1='tab:cyan', color_fpc1_s2='tab:orange', color_fpc2_s2='gold')
print("--------------------------------------------------- Bootstrap -------------------------------------------------------------------------------------------")
as1,as2 = bootstrap(A1_sample_window_combine_balanced, A2_sample_window_combine_balanced,"A","sample_window",features="CardAgeBin")
print("--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------")
create_pc_scores_plots(pc_scores_s1_A_sample_window, pc_scores_s2_A_sample_window, A1_sample_window_combine_balanced, A2_sample_window_combine_balanced,features="CardAgeBin")
S1 Explain variance PC1 (%): 99.54001643310664 S1 Explain variance PC2 (%): 0.13376186892582548 S2 Explain variance PC1 (%): 99.83602096130872 S2 Explain variance PC2 (%): 0.06238709532612137 The time series contributing most to PC1 is at index 800 with TestID 12529762.0 The time series contributing most to PC2 is at index 261 with TestID 12515884.0 The time series contributing most to PC1 is at index 140 with TestID 3568703 The time series contributing most to PC2 is at index 742 with TestID 3555912
--------------------------------------------------- Bootstrap ------------------------------------------------------------------------------------------- Confidence Interval of 1st component The number of sampling is 142 The boxplot of 1st Component
--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------
pc_scores_s1_B_cal_window, pc_scores_s2_B_cal_window,fpca_s1_B_cal_window,fpca_s2_B_cal_window = fpca_two_inputs(B1_cal_window_combine_balanced.iloc[:,:-6], B2_cal_window_combine_balanced.iloc[:,:-6], color_fpc1_s1='tab:blue', color_fpc2_s1='tab:cyan', color_fpc1_s2='tab:orange', color_fpc2_s2='gold')
print("--------------------------------------------------- Bootstrap -------------------------------------------------------------------------------------------")
bc1,bc2 = bootstrap(B1_cal_window_combine_balanced, B2_cal_window_combine_balanced,"B","cal_window",features="CardAgeBin")
print("--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------")
create_pc_scores_plots(pc_scores_s1_B_cal_window, pc_scores_s2_B_cal_window, B1_cal_window_combine_balanced, B2_cal_window_combine_balanced,features="CardAgeBin")
S1 Explain variance PC1 (%): 99.85065134319603 S1 Explain variance PC2 (%): 0.08925385168183501 S2 Explain variance PC1 (%): 99.87328890366544 S2 Explain variance PC2 (%): 0.09674564839625106 The time series contributing most to PC1 is at index 82 with TestID 12615989.0 The time series contributing most to PC2 is at index 664 with TestID 12371094.0 The time series contributing most to PC1 is at index 53 with TestID 3565690.0 The time series contributing most to PC2 is at index 53 with TestID 3565690.0
--------------------------------------------------- Bootstrap ------------------------------------------------------------------------------------------- Confidence Interval of 1st component The number of sampling is 142 The boxplot of 1st Component
--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------
pc_scores_s1_B_sample_window, pc_scores_s2_B_sample_window,fpca_s1_B_sample_window,fpca_s2_B_sample_window = fpca_two_inputs(B1_sample_window_combine_balanced.iloc[:,:-6], B2_sample_window_combine_balanced.iloc[:,:-6], color_fpc1_s1='tab:blue', color_fpc2_s1='tab:cyan', color_fpc1_s2='tab:orange', color_fpc2_s2='gold')
print("--------------------------------------------------- Bootstrap -------------------------------------------------------------------------------------------")
bs1,bs2 = bootstrap(B1_sample_window_combine_balanced, B2_sample_window_combine_balanced, "B","sample_window",features="CardAgeBin")
print("--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------")
create_pc_scores_plots(pc_scores_s1_B_sample_window, pc_scores_s2_B_sample_window, B1_sample_window_combine_balanced, B2_sample_window_combine_balanced,features="CardAgeBin")
S1 Explain variance PC1 (%): 99.79199457851556 S1 Explain variance PC2 (%): 0.05709964987162769 S2 Explain variance PC1 (%): 99.88982442479454 S2 Explain variance PC2 (%): 0.045673718167298656 The time series contributing most to PC1 is at index 684 with TestID 12191141.0 The time series contributing most to PC2 is at index 103 with TestID 12581955.0 The time series contributing most to PC1 is at index 666 with TestID 3518710.0 The time series contributing most to PC2 is at index 120 with TestID 3566587.0
--------------------------------------------------- Bootstrap ------------------------------------------------------------------------------------------- Confidence Interval of 1st component The number of sampling is 142 The boxplot of 1st Component
--------------------------------------------------- PCA Scores -------------------------------------------------------------------------------------------
df_list = []
def append_to_dataframe(window_name, slope1, slope2,se1,se2,n,p):
"""
Append regression analysis results to a global dataframe list.
"""
global df_list
df_list.append({'Window': window_name, 'Slope 1': slope1, 'Slope 2': slope2,'Se 1': se1, 'Se 2': se2, "N": n,"p_value":p})
append_to_dataframe('A_cal_window', *visualize_regression(fpca_s1_A_cal_window, fpca_s2_A_cal_window))
append_to_dataframe('A_sample_window', *visualize_regression(fpca_s1_A_sample_window, fpca_s2_A_sample_window))
append_to_dataframe('B_cal_window', *visualize_regression(fpca_s1_B_cal_window, fpca_s2_B_cal_window))
append_to_dataframe('B_sample_window', *visualize_regression(fpca_s1_B_sample_window, fpca_s2_B_sample_window))
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 7.930e+05
Date: Sun, 23 Jun 2024 Prob (F-statistic): 1.09e-83
Time: 22:40:34 Log-Likelihood: 242.45
No. Observations: 40 AIC: -480.9
Df Residuals: 38 BIC: -477.5
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0058 0.000 30.975 0.000 0.005 0.006
x1 -0.0071 7.93e-06 -890.531 0.000 -0.007 -0.007
==============================================================================
Omnibus: 3.406 Durbin-Watson: 0.109
Prob(Omnibus): 0.182 Jarque-Bera (JB): 3.120
Skew: 0.618 Prob(JB): 0.210
Kurtosis: 2.415 Cond. No. 48.0
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 8.806e+05
Date: Sun, 23 Jun 2024 Prob (F-statistic): 1.49e-84
Time: 22:40:34 Log-Likelihood: 244.49
No. Observations: 40 AIC: -485.0
Df Residuals: 38 BIC: -481.6
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0060 0.000 33.869 0.000 0.006 0.006
x1 -0.0071 7.53e-06 -938.384 0.000 -0.007 -0.007
==============================================================================
Omnibus: 5.735 Durbin-Watson: 0.083
Prob(Omnibus): 0.057 Jarque-Bera (JB): 3.128
Skew: 0.462 Prob(JB): 0.209
Kurtosis: 1.988 Cond. No. 48.0
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 5.446e+05
Date: Sun, 23 Jun 2024 Prob (F-statistic): 8.16e-52
Time: 22:40:34 Log-Likelihood: 146.38
No. Observations: 25 AIC: -288.8
Df Residuals: 23 BIC: -286.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0157 0.000 52.697 0.000 0.015 0.016
x1 -0.0148 2e-05 -737.942 0.000 -0.015 -0.015
==============================================================================
Omnibus: 0.529 Durbin-Watson: 0.661
Prob(Omnibus): 0.768 Jarque-Bera (JB): 0.461
Skew: -0.296 Prob(JB): 0.794
Kurtosis: 2.698 Cond. No. 30.8
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 7.501e+05
Date: Sun, 23 Jun 2024 Prob (F-statistic): 2.05e-53
Time: 22:40:34 Log-Likelihood: 150.62
No. Observations: 25 AIC: -297.2
Df Residuals: 23 BIC: -294.8
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0134 0.000 53.364 0.000 0.013 0.014
x1 -0.0147 1.69e-05 -866.059 0.000 -0.015 -0.015
==============================================================================
Omnibus: 3.255 Durbin-Watson: 0.195
Prob(Omnibus): 0.196 Jarque-Bera (JB): 2.209
Skew: 0.543 Prob(JB): 0.331
Kurtosis: 2.029 Cond. No. 30.8
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 2.793e+05
Date: Sun, 23 Jun 2024 Prob (F-statistic): 7.17e-156
Time: 22:40:34 Log-Likelihood: 499.94
No. Observations: 90 AIC: -995.9
Df Residuals: 88 BIC: -990.9
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -0.0001 0.000 -0.508 0.613 -0.001 0.000
x1 0.0020 3.84e-06 528.450 0.000 0.002 0.002
==============================================================================
Omnibus: 13.947 Durbin-Watson: 0.016
Prob(Omnibus): 0.001 Jarque-Bera (JB): 8.997
Skew: -0.629 Prob(JB): 0.0111
Kurtosis: 2.097 Cond. No. 106.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.999
Model: OLS Adj. R-squared: 0.999
Method: Least Squares F-statistic: 1.663e+05
Date: Sun, 23 Jun 2024 Prob (F-statistic): 5.68e-146
Time: 22:40:34 Log-Likelihood: 477.27
No. Observations: 90 AIC: -950.5
Df Residuals: 88 BIC: -945.5
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0008 0.000 2.973 0.004 0.000 0.001
x1 0.0020 4.94e-06 407.824 0.000 0.002 0.002
==============================================================================
Omnibus: 11.543 Durbin-Watson: 0.009
Prob(Omnibus): 0.003 Jarque-Bera (JB): 9.163
Skew: -0.675 Prob(JB): 0.0102
Kurtosis: 2.211 Cond. No. 106.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.999
Model: OLS Adj. R-squared: 0.999
Method: Least Squares F-statistic: 1.747e+04
Date: Sun, 23 Jun 2024 Prob (F-statistic): 2.40e-28
Time: 22:40:34 Log-Likelihood: 83.320
No. Observations: 20 AIC: -162.6
Df Residuals: 18 BIC: -160.6
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0128 0.002 6.937 0.000 0.009 0.017
x1 -0.0203 0.000 -132.177 0.000 -0.021 -0.020
==============================================================================
Omnibus: 2.319 Durbin-Watson: 0.138
Prob(Omnibus): 0.314 Jarque-Bera (JB): 1.832
Skew: 0.609 Prob(JB): 0.400
Kurtosis: 2.154 Cond. No. 25.0
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.999
Model: OLS Adj. R-squared: 0.999
Method: Least Squares F-statistic: 1.861e+04
Date: Sun, 23 Jun 2024 Prob (F-statistic): 1.36e-28
Time: 22:40:34 Log-Likelihood: 83.924
No. Observations: 20 AIC: -163.8
Df Residuals: 18 BIC: -161.9
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0131 0.002 7.367 0.000 0.009 0.017
x1 -0.0203 0.000 -136.433 0.000 -0.021 -0.020
==============================================================================
Omnibus: 2.598 Durbin-Watson: 0.133
Prob(Omnibus): 0.273 Jarque-Bera (JB): 1.958
Skew: 0.617 Prob(JB): 0.376
Kurtosis: 2.092 Cond. No. 25.0
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
slopes_df = pd.DataFrame(df_list)
slopes_df
| Window | Slope 1 | Slope 2 | Se 1 | Se 2 | N | p_value | |
|---|---|---|---|---|---|---|---|
| 0 | A_cal_window | -0.007061 | -0.007069 | 0.000008 | 0.000008 | 40 | 0.44 |
| 1 | A_sample_window | -0.014793 | -0.014652 | 0.000020 | 0.000017 | 25 | 0.00 |
| 2 | B_cal_window | 0.002030 | 0.002015 | 0.000004 | 0.000005 | 90 | 0.02 |
| 3 | B_sample_window | -0.020282 | -0.020312 | 0.000153 | 0.000149 | 20 | 0.89 |
This is another functional Data Analysis method. Unlike FPCA, the following analysis utilizes the entire time series in a balanced and centered dataset as response variables for regression with the features grouped by bins. This is done to distinguish between two systems under the influence of features.
These are the coefficients from the output of the model.
print("System 1:")
A1_cal_window_funct_reg = Function_regression(A1_cal_window_combine_balanced,40,['AgeOfCardInDaysAtTimeOfTest'])
print("----------------------------------------------------------------------------")
print("\n","System 2:")
A2_cal_window_funct_reg = Function_regression(A2_cal_window_combine_balanced,40,['AgeOfCardInDaysAtTimeOfTest'])
System 1:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 39.0),), n_basis=41, period=39.0),
coefficients=[[ 5.44831087e-01 -2.48517680e-01 -3.73647104e-02 -1.03891504e-01
-2.58439000e-02 -5.99697051e-02 -2.65371333e-03 -7.00853023e-02
9.57908317e-03 -5.51903945e-02 8.00488064e-03 -8.65443174e-02
-8.70556984e-03 -3.42938125e-02 -3.66511518e-02 -3.07548887e-02
4.96307464e-04 -5.53743332e-02 -4.09042855e-02 -2.42214352e-02
-8.89843291e-03 -4.75685312e-02 4.60845094e-03 -2.92784615e-02
-1.39147659e-02 -3.74305179e-02 -4.76644256e-02 -3.03830126e-02
-2.91756320e-03 -3.78845803e-02 6.71415720e-03 -9.21303261e-02
-1.40742815e-02 -1.01446250e-01 -8.15209354e-03 -1.64676788e-01
-8.51399471e-03 -2.53666543e+13 2.99952283e+11 -2.53666543e+13
-2.99952283e+11]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 39.0),), n_basis=41, period=39.0),
coefficients=[[ 1.18738419e-02 -5.55202998e-03 -7.12022128e-04 -2.01225702e-03
-6.61002740e-04 -1.27536169e-03 1.30976241e-04 -9.66391188e-04
3.46259348e-04 -1.14881492e-03 1.55435324e-04 -8.70642605e-04
-1.69066303e-04 -8.00293848e-04 2.84906358e-05 -6.45470177e-04
-8.68556409e-05 -4.06860407e-04 3.85114633e-04 -9.96990616e-04
2.53289787e-04 -8.67523746e-04 1.00469545e-04 -8.74869444e-04
-8.45185813e-05 -6.43713834e-04 5.97328159e-05 -9.55442707e-04
3.00038413e-05 -1.11627423e-03 5.11032860e-04 -1.56760635e-03
4.87036834e-04 -2.56032343e-03 -1.89085071e-04 -3.50338940e-03
-1.85204082e-04 -5.35453548e+11 6.33156082e+09 -5.35453548e+11
-6.33156082e+09]])
----------------------------------------------------------------------------
System 2:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 39.0),), n_basis=41, period=39.0),
coefficients=[[ 4.72310867e-01 -2.37365658e-01 -2.29396697e-02 -9.99958519e-02
-2.76898793e-02 -4.65937857e-02 4.26908362e-03 -5.33222306e-02
2.80346162e-02 -6.79134955e-02 2.86997462e-02 -6.85677626e-02
3.11028938e-03 -5.02731685e-02 2.72785356e-02 2.79043366e-03
2.78878282e-02 2.95297674e-04 1.17621366e-02 -2.18320684e-02
3.98484811e-02 -8.32573466e-02 2.20214534e-02 -2.61056086e-02
-4.82826156e-03 8.78993517e-03 -1.82064246e-02 8.84172669e-03
1.45998829e-02 -5.31498017e-02 1.19681365e-02 -6.52269710e-02
1.31741005e-02 -1.39051936e-01 -1.39764898e-02 -1.33792448e-01
-5.72656980e-02 -2.31724916e+13 2.74007036e+11 -2.31724916e+13
-2.74007036e+11]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 39.0),), n_basis=41, period=39.0),
coefficients=[[ 1.47748435e-02 -6.88741729e-03 -8.12301186e-04 -2.47091351e-03
-7.38218480e-04 -1.68662050e-03 1.52403969e-04 -1.38267931e-03
3.07366183e-04 -1.24752567e-03 6.91503697e-05 -1.29602409e-03
-3.20771930e-04 -9.57715979e-04 -5.09968479e-04 -1.08670242e-03
-3.51221107e-04 -9.35432749e-04 -6.53541798e-05 -1.20088600e-03
-4.82059248e-05 -8.09957732e-04 -3.22529885e-05 -1.10443840e-03
-2.42517985e-04 -1.23124520e-03 -1.89463087e-04 -1.36358304e-03
-9.49074684e-05 -1.28854051e-03 4.94784472e-04 -2.05294459e-03
3.46129739e-04 -2.88283496e-03 -2.23840909e-04 -4.56072005e-03
1.50559251e-04 -6.72856470e+11 7.95630485e+09 -6.72856470e+11
-7.95630485e+09]])
print("System 1:")
A1_sample_window_funct_reg = Function_regression(A1_sample_window_combine_balanced,25,["AgeOfCardInDaysAtTimeOfTest"])
print("----------------------------------------------------------------------------")
print("\n","System 2:")
A2_sample_window_funct_reg = Function_regression(A2_sample_window_combine_balanced,25,["AgeOfCardInDaysAtTimeOfTest"])
System 1:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 24.0),), n_basis=25, period=24.0),
coefficients=[[-3.47405267e-01 9.45639274e-02 6.96805443e-02 -3.41192074e-02
1.35924638e-02 -7.74780484e-02 -4.10167328e-02 -1.16125792e-02
-9.53707165e-02 -7.81899937e-02 -2.43494384e-01 2.55393357e-01
-8.78382363e-02 -1.03298321e-02 1.69542022e-02 1.00396395e-01
9.25932670e-03 9.91599491e-02 5.82284577e-02 8.11088770e-02
1.22798698e-01 2.13497360e-01 3.75288394e-02 1.19839537e+14
2.30508497e-01]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 24.0),), n_basis=25, period=24.0),
coefficients=[[ 3.83486978e-03 -1.28794880e-03 -7.82546285e-04 1.31167284e-04
-1.02832165e-04 9.68728150e-04 5.59264870e-04 -8.66213788e-05
1.10147068e-03 1.00261966e-03 3.26236614e-03 -3.66247700e-03
1.07275973e-03 -1.58717448e-04 -4.67277915e-04 -1.49344973e-03
-5.33692231e-06 -1.39933620e-03 -6.89587321e-04 -1.52795476e-03
-1.40133434e-03 -2.67820855e-03 -7.79961720e-04 -1.69909044e+12
-3.25960820e-03]])
----------------------------------------------------------------------------
System 2:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 24.0),), n_basis=25, period=24.0),
coefficients=[[ 2.27267912e-01 -9.49063655e-02 -2.51954581e-02 -9.26852018e-03
-1.23526635e-02 -1.52229697e-02 6.31371005e-02 -1.73891287e-01
2.65736930e-02 4.31894900e-03 2.27511466e-02 -1.69114550e-01
1.17173387e-01 -1.76855750e-01 -4.07989176e-02 -4.27431202e-02
-8.38436819e-02 -3.42118956e-02 -9.75115518e-02 -1.55541589e-01
-6.37413492e-02 -1.55948522e-01 1.46022119e-01 -8.00315331e+13
-1.22042466e-01]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 24.0),), n_basis=25, period=24.0),
coefficients=[[ 5.19883123e-03 -1.48621696e-03 -1.60281428e-03 -3.85195201e-04
-1.73855531e-04 1.67866379e-03 3.08372260e-04 9.96956359e-04
1.52496540e-03 1.70474957e-03 5.49096855e-03 -6.06508302e-03
6.25321914e-04 2.70277003e-04 -1.12044687e-03 -2.93449431e-03
1.27256199e-03 -2.33846456e-03 -1.22490320e-04 -2.69124677e-03
-1.57259327e-03 -3.26346222e-03 -3.22476788e-03 -2.59648512e+12
-5.20346777e-03]])
print("System 1:")
B1_cal_window_funct_reg = Function_regression(B1_cal_window_combine_balanced,90,["AgeOfCardInDaysAtTimeOfTest"])
print("----------------------------------------------------------------------------")
print("\n","System 2:")
B2_cal_window_funct_reg = Function_regression(B2_cal_window_combine_balanced,90,["AgeOfCardInDaysAtTimeOfTest"])
System 1:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 89.0),), n_basis=91, period=89.0),
coefficients=[[ 1.41944188e+01 -6.18075643e+00 -1.30919887e+00 -2.39368608e+00
-1.83134625e-01 -2.36676515e+00 3.97693796e-01 -1.41883728e+00
-5.40517823e-01 -4.95265371e-01 -4.54411238e-01 -3.50507286e-01
1.08951474e+00 -7.64794470e-01 6.79133545e-01 -8.38301554e-01
6.22457016e-02 -5.87978400e-01 4.96112543e-01 -8.72747297e-01
1.05314002e+00 -1.32193016e+00 6.16687582e-01 -1.60670875e+00
7.05988157e-02 -1.82184111e+00 9.95172623e-02 -1.30109812e+00
-5.05472751e-01 -1.13295633e+00 -5.26193256e-01 -9.51463359e-01
-9.00683786e-01 -8.53833431e-01 -3.43621093e-01 -1.19133676e+00
-1.02012295e+00 2.68934625e-01 -1.66048368e+00 4.30706708e-01
-4.55529504e-01 -4.28099111e-01 -1.92364062e-01 -5.01679667e-01
-7.34823350e-01 -9.58270947e-02 -5.64465162e-01 -9.19193356e-02
-5.62647501e-01 4.29272744e-01 -7.63253088e-01 8.70708624e-01
-6.69852477e-01 4.53599282e-01 7.00751391e-02 3.40961395e-01
2.66664619e-01 2.16600466e-01 4.13542503e-01 1.40006634e-01
2.69372763e-01 -5.17469534e-01 2.13189244e-01 -8.36191263e-02
6.51723684e-01 -3.10098693e-01 4.86352995e-01 -3.90751186e-01
2.03664818e-02 -8.39404382e-01 -3.88608894e-02 -7.22326990e-01
4.32829163e-01 -6.49650857e-01 4.71450017e-01 -6.61520497e-01
1.86597075e-01 -1.86009072e+00 -2.73574183e-01 -1.42965988e+00
-5.07028944e-01 -2.38608382e-01 -6.04082448e-01 -1.28647030e+00
-3.43943548e-01 -2.28631365e+00 1.43353149e-01 -4.88518865e+14
4.14401855e+11 -4.88518865e+14 -4.14401855e+11]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 89.0),), n_basis=91, period=89.0),
coefficients=[[ 2.77308778e-03 -3.02275603e-04 1.13051320e-04 -4.07613079e-05
-1.83789224e-04 6.55023869e-04 4.78400511e-04 -7.73109568e-04
-1.68673965e-04 3.44093887e-04 -7.41888422e-04 -1.31276533e-03
2.02504134e-04 -1.59577018e-03 3.23105442e-04 -2.06541984e-04
-5.44847302e-04 -1.24398518e-03 1.36200440e-04 -1.92718742e-03
6.19120804e-05 -4.25941449e-04 -7.14207934e-04 1.38951279e-03
7.43407211e-04 1.44489427e-04 6.43915403e-04 -1.21858565e-03
1.38392509e-04 -6.86304157e-04 -6.51953881e-04 6.96336843e-04
-1.03930699e-04 -6.23372649e-04 -1.63625061e-04 -9.81770329e-04
-4.27855658e-04 -1.54221357e-03 6.06777390e-04 -3.17103293e-04
5.58214446e-04 -6.74405462e-05 -4.07873680e-05 -4.45098304e-04
-7.48285019e-04 5.16660497e-04 -1.01901838e-03 4.29369174e-05
-7.59435042e-04 -1.29698468e-03 2.82353057e-04 2.34173143e-04
-6.38391899e-05 4.20394202e-04 3.49486815e-04 -1.07113687e-04
-1.25112525e-04 1.15613800e-03 -1.17631525e-05 -2.57567907e-04
7.45550452e-04 1.04591972e-03 6.70687354e-04 -4.19236563e-04
-4.60616753e-04 -8.89591011e-04 3.40731861e-04 -1.79128094e-04
7.13527816e-04 -1.77897435e-05 9.91017163e-04 2.46021428e-04
-7.41851710e-04 -2.01694303e-04 -3.78495391e-04 -1.82882975e-03
-6.56182562e-04 1.15475275e-03 -8.57988004e-04 7.61039968e-04
-7.86394694e-04 -3.98487928e-04 6.13705975e-04 -1.06347249e-03
7.79397035e-04 -1.35696275e-03 4.05315476e-04 -9.07723879e+10
7.70006004e+07 -9.07723879e+10 -7.70006004e+07]])
----------------------------------------------------------------------------
System 2:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 89.0),), n_basis=91, period=89.0),
coefficients=[[ 1.71568135e+01 -7.12105429e+00 -1.55871797e+00 -2.79740396e+00
-2.15912051e-01 -2.80706127e+00 5.42959608e-01 -1.84733622e+00
-5.98957210e-01 -6.63148840e-01 -7.37373742e-01 -6.12628835e-01
1.23517903e+00 -1.13236325e+00 8.15547052e-01 -8.89289354e-01
1.62516803e-01 -6.42451128e-01 5.01874847e-01 -1.16529209e+00
1.34854437e+00 -1.43012546e+00 6.69080449e-01 -1.75753214e+00
1.57711185e-01 -2.09626737e+00 2.11458691e-01 -1.61611372e+00
-4.03767548e-01 -1.56894793e+00 -8.14529808e-01 -1.16193989e+00
-1.07491135e+00 -1.18209198e+00 -3.77325897e-01 -1.52136322e+00
-1.38606618e+00 -1.59806700e-01 -1.88046769e+00 4.11117985e-01
-4.20426161e-01 -4.73961643e-01 -2.61184762e-01 -6.35294867e-01
-9.11369931e-01 1.03399251e-01 -8.83326887e-01 -6.71962007e-02
-7.99699171e-01 3.86520671e-01 -9.24469078e-01 1.16517878e+00
-7.84055618e-01 6.83272312e-01 2.17260909e-01 3.95777948e-01
2.46851758e-01 5.64912734e-01 5.28764385e-01 1.81467775e-01
3.06654834e-01 -4.20326101e-01 2.84649025e-01 1.42305409e-02
6.20488061e-01 -3.17726804e-01 5.45232688e-01 -5.64309285e-01
1.50569772e-01 -1.09371131e+00 1.73983824e-01 -8.13898495e-01
4.36953860e-01 -9.39762811e-01 3.93244656e-01 -1.22890210e+00
-2.57587822e-02 -2.23930604e+00 -4.19982626e-01 -1.39309666e+00
-6.12658396e-01 -3.46651093e-01 -5.66124789e-01 -1.49707973e+00
-3.02226452e-01 -2.90835120e+00 3.20798153e-01 -5.88305340e+14
4.99048945e+11 -5.88305340e+14 -4.99048945e+11]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 89.0),), n_basis=91, period=89.0),
coefficients=[[-3.19169018e-04 -1.17826466e-03 1.20249396e-04 2.20942726e-04
-2.26451277e-04 1.04685986e-03 -5.05308549e-06 5.20791011e-04
-5.32174834e-04 8.14911722e-04 5.93846886e-04 6.71645274e-06
4.08971977e-04 -1.98491439e-04 3.91884955e-04 -8.05234342e-04
-1.43785817e-03 -1.93489640e-03 6.44847207e-04 -9.10974402e-04
-6.69561678e-04 -1.78917124e-03 -2.99048740e-04 5.21031945e-04
4.28242059e-04 1.46643074e-04 -2.09481053e-04 -6.96994361e-04
-1.16849198e-03 9.84824280e-04 5.17550617e-04 1.00392962e-03
-1.98732189e-04 8.19320004e-04 -3.59142983e-04 1.81618516e-04
1.31458903e-03 1.68764939e-03 2.51197033e-04 2.87032217e-04
-8.21393697e-05 -5.07134449e-04 4.02276678e-04 -3.49579255e-04
-6.04589628e-04 -1.17088026e-03 2.74599394e-04 -1.03717045e-04
1.08480416e-04 -3.38030455e-04 5.52205361e-04 -8.29760457e-04
-1.05675894e-04 -3.09141357e-04 -5.87936673e-04 -1.01212529e-04
3.26107231e-04 -9.58560086e-04 -1.50549070e-04 -2.56941177e-04
9.68344389e-04 -1.85509372e-04 4.27845169e-04 -7.88548511e-04
5.79180113e-04 -1.09217207e-03 5.92050633e-04 7.78146109e-04
-8.93308793e-05 6.44044159e-04 -7.88796076e-04 -3.95799553e-05
-4.26592200e-04 1.48979573e-03 6.14249288e-04 1.50519927e-03
8.28337352e-04 1.96166939e-03 -3.48373980e-04 -1.79282175e-03
-9.20258848e-04 3.71348472e-05 -2.55227829e-04 -1.37972657e-03
-1.24669112e-04 2.45679192e-04 -2.72785877e-04 3.33713572e+09
-2.83083281e+06 3.33713572e+09 2.83083281e+06]])
print("System 1:")
B1_sample_window_funct_reg = Function_regression(B1_sample_window_combine_balanced,20,["AgeOfCardInDaysAtTimeOfTest"])
print("----------------------------------------------------------------------------")
print("\n","System 2:")
B2_sample_window_funct_reg = Function_regression(B2_sample_window_combine_balanced,20,["AgeOfCardInDaysAtTimeOfTest"])
System 1:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 19.0),), n_basis=21, period=19.0),
coefficients=[[ 1.94477262e+00 -5.74698778e-01 4.94399705e-01 -1.88917790e-01
4.59279146e-01 -4.46228280e-01 4.80121074e-01 -3.09173927e-01
2.84898091e-01 -4.26428562e-01 4.60382637e-01 -1.77049198e-01
4.30580453e-01 -2.28338562e-01 2.39491499e-01 -3.79670013e-01
3.09234260e-01 -4.73380784e+14 2.33768288e+12 -4.73380784e+14
-2.33768288e+12]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 19.0),), n_basis=21, period=19.0),
coefficients=[[-7.09581020e-04 -8.68061993e-04 -3.74666503e-04 -8.59587528e-04
-3.89071731e-04 6.07273996e-04 -5.45706512e-04 6.85532296e-04
2.66439598e-04 7.82302116e-04 -1.00400795e-03 -1.08968462e-03
-6.22492728e-04 -9.25278571e-05 6.79326947e-04 -1.04001312e-03
6.94320739e-04 1.28710581e+11 -6.35607808e+08 1.28710581e+11
6.35607808e+08]])
----------------------------------------------------------------------------
System 2:
Model Summary:
Intercept: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 19.0),), n_basis=21, period=19.0),
coefficients=[[ 2.35854382e+00 -1.05727397e+00 5.17485389e-01 -3.08207946e-01
4.18197900e-01 -3.80737342e-01 4.77544884e-01 -1.89795445e-01
3.25098513e-01 -4.29825818e-01 3.26121332e-01 -2.56410164e-01
4.09545358e-01 -2.97515899e-01 2.90183483e-01 -7.19536575e-01
3.39351987e-01 -5.67897786e+14 2.80443351e+12 -5.67897786e+14
-2.80443351e+12]])
Coefficient of AgeOfCardInDaysAtTimeOfTest: FDataBasis(
_basis=FourierBasis(domain_range=((0.0, 19.0),), n_basis=21, period=19.0),
coefficients=[[-8.82368361e-04 1.58050863e-03 1.69679372e-04 -9.60658336e-04
6.18075451e-04 -3.04489263e-04 -4.07719307e-04 -2.19890657e-04
4.60177294e-04 3.13117904e-04 7.77356798e-04 -5.96044021e-04
5.66543695e-04 -4.32255887e-04 9.78368234e-04 8.73780471e-04
9.06883416e-04 7.67085169e+10 -3.78807491e+08 7.67085169e+10
3.78807491e+08]])
coefficent_visualization(A1_cal_window_funct_reg,A2_cal_window_funct_reg,["AgeOfCardInDaysAtTimeOfTest"],range(1,36),"SensorA Cal window")
coefficent_visualization(A1_sample_window_funct_reg,A2_sample_window_funct_reg,["AgeOfCardInDaysAtTimeOfTest"],range(1,23),"SensorA sample window")
coefficent_visualization(B1_cal_window_funct_reg,B2_cal_window_funct_reg,["AgeOfCardInDaysAtTimeOfTest"],range(1,86),"SensorB Cal window")
coefficent_visualization(B1_sample_window_funct_reg, B2_sample_window_funct_reg, ["AgeOfCardInDaysAtTimeOfTest"], range(1, 16), "SensorB Sample window")